@shamdasani/

# Linear Regression

## No description

Files
• main.py
• graph.png
main.py
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```
```from statistics import mean
import numpy as np

x_values = np.array([1,2,3,4,5,6,7,8,9,10], dtype=np.float64)
y_values = np.array([1,4,1,6,4,7,4,6,10,8], dtype=np.float64)

def best_fit_line(x_values,y_values):
m = (((mean(x_values)*mean(y_values)) - mean(x_values*y_values)) /
((mean(x_values)*mean(x_values)) - mean(x_values*x_values)))

b = mean(y_values) - m*mean(x_values)

return m, b

m, b = best_fit_line(x_values,y_values)

print("regression line: " + "y = " + str(round(m,2)) + "x + " + str(round(b,2)) )

# Prediction
x_prediction = 15
y_prediction = (m*x_prediction)+b
print("predicted coordinate: (" + str(round(x_prediction,2)) + ", " + str(round(y_prediction,2)) + ")")

# y values of regression line
regression_line = [(m*x)+b for x in x_values]

# R Squared Error
def squared_error(ys_orig, ys_line):
return sum((ys_line - ys_orig) * (ys_line - ys_orig))

def r_squared_value(ys_orig,ys_line):
squared_error_regr = squared_error(ys_orig, ys_line) # squared error of regression line
y_mean_line = [mean(ys_orig) for y in ys_orig] # horizontal line (mean of y values)
squared_error_y_mean = squared_error(ys_orig, y_mean_line) # squared error of the mean horizontal line
return 1 - (squared_error_regr/squared_error_y_mean)

r_squared = r_squared_value(y_values,regression_line)
print("r^2 value: " + str(r_squared))

# Plotting
import matplotlib.pyplot as plt
from matplotlib import style
style.use('seaborn')

plt.title('Linear Regression')
plt.scatter(x_values,y_values,color='#5b9dff',label='data')
plt.scatter(x_prediction, y_prediction, color='#fc003f', label="predicted")
plt.plot(x_values, regression_line, color='000000', label='regression line')
plt.legend(loc=4)
plt.savefig("graph.png")```